Question

Plot each point given in polar coordinates.

$\left(-4,\frac{\pi }{3}\right)$

Short answer

We can plot the given polar coordinate $\left(-4,\frac{\pi }{3}\right)$as following :-

Step-by-step solution

Step 1. Given Information

We have given the following polar coordinate :-

$\left(-4,\frac{\pi }{3}\right)$

We have to plot this polar coordinate.

Step 2. Plot the point on graph   

We know that polar coordinate is of the form $\left(r,\theta \right)$, where $r$represents the distance at which the point is with respect to the origin and $\theta$is the angle at which it is with respect to the polar axis.

As the $-4$is negative, so that the point will lie in third quadrant.

Then the angle will be :-

$$\begin{gathered} \pi +\frac{\pi }{3} \\ ={180}^o+\frac{{180}^o}{3} \\ ={180}^o+{60}^o \\ ={240}^o \end{gathered}$$

So we can plot the given point$\left(-4,\frac{\pi }{3}\right)$as following :-